%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB030+2 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:29:42 AM UTC 2025
% Result : Unsatisfiable 0.14s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWB030+2 : TPTP v9.0.0. Released v5.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 07:53:10 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.39 % SZS status Unsatisfiable
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 tff(icext_type, type, (
% 0.14/0.39 icext: ( $i * $i ) > $o)).
% 0.14/0.39 tff(uri_ex_c_type, type, (
% 0.14/0.39 uri_ex_c: $i)).
% 0.14/0.39 tff(iext_type, type, (
% 0.14/0.39 iext: ( $i * $i * $i ) > $o)).
% 0.14/0.39 tff(uri_rdf_type_type, type, (
% 0.14/0.39 uri_rdf_type: $i)).
% 0.14/0.39 tff(tptp_fun_BNODE_x_0_type, type, (
% 0.14/0.39 tptp_fun_BNODE_x_0: $i)).
% 0.14/0.39 tff(literal_typed_type, type, (
% 0.14/0.39 literal_typed: ( $i * $i ) > $i)).
% 0.14/0.39 tff(uri_xsd_boolean_type, type, (
% 0.14/0.39 uri_xsd_boolean: $i)).
% 0.14/0.39 tff(dat_str_true_type, type, (
% 0.14/0.39 dat_str_true: $i)).
% 0.14/0.39 tff(uri_owl_hasSelf_type, type, (
% 0.14/0.39 uri_owl_hasSelf: $i)).
% 0.14/0.39 tff(uri_owl_onProperty_type, type, (
% 0.14/0.39 uri_owl_onProperty: $i)).
% 0.14/0.39 tff(uri_owl_Restriction_type, type, (
% 0.14/0.39 uri_owl_Restriction: $i)).
% 0.14/0.39 tff(uri_owl_complementOf_type, type, (
% 0.14/0.39 uri_owl_complementOf: $i)).
% 0.14/0.39 tff(uri_owl_Class_type, type, (
% 0.14/0.39 uri_owl_Class: $i)).
% 0.14/0.39 tff(ic_type, type, (
% 0.14/0.39 ic: $i > $o)).
% 0.14/0.39 tff(1,assumption,(~iext(uri_rdf_type, uri_ex_c, uri_ex_c)), introduced(assumption)).
% 0.14/0.39 tff(2,plain,
% 0.14/0.39 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(3,plain,
% 0.14/0.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.14/0.39 tff(4,plain,
% 0.14/0.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(5,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rdfs_cext_def')).
% 0.14/0.39 tff(6,plain,
% 0.14/0.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.14/0.39 tff(7,plain,(
% 0.14/0.39 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.14/0.39 inference(skolemize,[status(sab)],[6])).
% 0.14/0.39 tff(8,plain,
% 0.14/0.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.14/0.39 tff(9,plain,
% 0.14/0.39 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_c, uri_ex_c) <=> icext(uri_ex_c, uri_ex_c))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(10,plain,
% 0.14/0.39 (iext(uri_rdf_type, uri_ex_c, uri_ex_c) <=> icext(uri_ex_c, uri_ex_c)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.14/0.39 tff(11,plain,
% 0.14/0.39 ((~(iext(uri_rdf_type, uri_ex_c, uri_ex_c) <=> icext(uri_ex_c, uri_ex_c))) | iext(uri_rdf_type, uri_ex_c, uri_ex_c) | (~icext(uri_ex_c, uri_ex_c))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(12,plain,
% 0.14/0.39 (iext(uri_rdf_type, uri_ex_c, uri_ex_c) | (~icext(uri_ex_c, uri_ex_c))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.14/0.39 tff(13,plain,
% 0.14/0.39 (~icext(uri_ex_c, uri_ex_c)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[12, 1])).
% 0.14/0.39 tff(14,plain,
% 0.14/0.39 (?[BNODE_x: $i] : (iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type) & iext(uri_owl_hasSelf, BNODE_x, literal_typed(dat_str_true, uri_xsd_boolean))) <=> ?[BNODE_x: $i] : (iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type) & iext(uri_owl_hasSelf, BNODE_x, literal_typed(dat_str_true, uri_xsd_boolean)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(15,plain,
% 0.14/0.39 (^[BNODE_x: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x)) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction)) <=> (iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction))), ((((iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x)) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type)) <=> ((iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type)))), rewrite(((iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type)) <=> (iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type))), ((((iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x)) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type)) <=> (iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type)))), (((((iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x)) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type)) & iext(uri_owl_hasSelf, BNODE_x, literal_typed(dat_str_true, uri_xsd_boolean))) <=> ((iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type)) & iext(uri_owl_hasSelf, BNODE_x, literal_typed(dat_str_true, uri_xsd_boolean))))), rewrite(((iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type)) & iext(uri_owl_hasSelf, BNODE_x, literal_typed(dat_str_true, uri_xsd_boolean))) <=> (iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type) & iext(uri_owl_hasSelf, BNODE_x, literal_typed(dat_str_true, uri_xsd_boolean)))), (((((iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x)) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type)) & iext(uri_owl_hasSelf, BNODE_x, literal_typed(dat_str_true, uri_xsd_boolean))) <=> (iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type) & iext(uri_owl_hasSelf, BNODE_x, literal_typed(dat_str_true, uri_xsd_boolean)))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(16,plain,
% 0.14/0.39 (?[BNODE_x: $i] : ((((iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x)) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type)) & iext(uri_owl_hasSelf, BNODE_x, literal_typed(dat_str_true, uri_xsd_boolean))) <=> ?[BNODE_x: $i] : (iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type) & iext(uri_owl_hasSelf, BNODE_x, literal_typed(dat_str_true, uri_xsd_boolean)))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.14/0.39 tff(17,axiom,(?[BNODE_x: $i] : ((((iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x)) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type)) & iext(uri_owl_hasSelf, BNODE_x, literal_typed(dat_str_true, uri_xsd_boolean)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','testcase_premise_fullish_030_Bad_Class')).
% 0.14/0.39 tff(18,plain,
% 0.14/0.39 (?[BNODE_x: $i] : (iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type) & iext(uri_owl_hasSelf, BNODE_x, literal_typed(dat_str_true, uri_xsd_boolean)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (?[BNODE_x: $i] : (iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x) & iext(uri_rdf_type, BNODE_x, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_x, uri_rdf_type) & iext(uri_owl_hasSelf, BNODE_x, literal_typed(dat_str_true, uri_xsd_boolean)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.14/0.40 tff(20,plain,(
% 0.14/0.40 iext(uri_rdf_type, uri_ex_c, uri_owl_Class) & iext(uri_owl_complementOf, uri_ex_c, BNODE_x!0) & iext(uri_rdf_type, BNODE_x!0, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_x!0, uri_rdf_type) & iext(uri_owl_hasSelf, BNODE_x!0, literal_typed(dat_str_true, uri_xsd_boolean))),
% 0.14/0.40 inference(skolemize,[status(sab)],[19])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (iext(uri_owl_hasSelf, BNODE_x!0, literal_typed(dat_str_true, uri_xsd_boolean))),
% 0.14/0.40 inference(and_elim,[status(thm)],[20])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 (iext(uri_owl_onProperty, BNODE_x!0, uri_rdf_type)),
% 0.14/0.40 inference(and_elim,[status(thm)],[20])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 (^[Z: $i, P: $i, V: $i] : rewrite((![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P))) <=> ((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 (![Z: $i, P: $i, V: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P))) <=> ![Z: $i, P: $i, V: $i] : ((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 (^[Z: $i, P: $i, V: $i] : refl((![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P))) <=> (![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 (![Z: $i, P: $i, V: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P))) <=> ![Z: $i, P: $i, V: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 (^[Z: $i, P: $i, V: $i] : rewrite((![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P))) <=> (![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 (![Z: $i, P: $i, V: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P))) <=> ![Z: $i, P: $i, V: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (![Z: $i, P: $i, V: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P))) <=> ![Z: $i, P: $i, V: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)))),
% 0.14/0.40 inference(transitivity,[status(thm)],[28, 26])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (^[Z: $i, P: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P)) <=> (~((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P))))), ((~(iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P))) <=> (~(~((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P))))))), rewrite((~(~((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P))))) <=> ((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)))), ((~(iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P))) <=> ((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P))))), (((~(iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X))) <=> (((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X))))), rewrite((((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X))) <=> (![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)))), (((~(iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X))) <=> (![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 (![Z: $i, P: $i, V: $i] : ((~(iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X))) <=> ![Z: $i, P: $i, V: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.14/0.40 tff(32,plain,
% 0.14/0.40 (![Z: $i, P: $i, V: $i] : ((~(iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X))) <=> ![Z: $i, P: $i, V: $i] : ((~(iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 (^[Z: $i, P: $i, V: $i] : rewrite(((iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> iext(P, X, X))) <=> ((~(iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(34,plain,
% 0.14/0.40 (![Z: $i, P: $i, V: $i] : ((iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> iext(P, X, X))) <=> ![Z: $i, P: $i, V: $i] : ((~(iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.14/0.40 tff(35,axiom,(![Z: $i, P: $i, V: $i] : ((iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_restrict_hasself')).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 (![Z: $i, P: $i, V: $i] : ((~(iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 (![Z: $i, P: $i, V: $i] : ((~(iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.14/0.40 tff(38,plain,(
% 0.14/0.40 ![Z: $i, P: $i, V: $i] : ((~(iext(uri_owl_hasSelf, Z, V) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[37])).
% 0.14/0.40 tff(39,plain,
% 0.14/0.40 (![Z: $i, P: $i, V: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 (![Z: $i, P: $i, V: $i] : (![X: $i] : (icext(Z, X) <=> iext(P, X, X)) | (~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (![Z: $i, P: $i, V: $i] : ((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[40, 24])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 (((~![Z: $i, P: $i, V: $i] : ((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))) | (![X: $i] : (icext(BNODE_x!0, X) <=> iext(uri_rdf_type, X, X)) | (~iext(uri_owl_onProperty, BNODE_x!0, uri_rdf_type)) | (~iext(uri_owl_hasSelf, BNODE_x!0, literal_typed(dat_str_true, uri_xsd_boolean))))) <=> ((~![Z: $i, P: $i, V: $i] : ((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))) | ![X: $i] : (icext(BNODE_x!0, X) <=> iext(uri_rdf_type, X, X)) | (~iext(uri_owl_onProperty, BNODE_x!0, uri_rdf_type)) | (~iext(uri_owl_hasSelf, BNODE_x!0, literal_typed(dat_str_true, uri_xsd_boolean))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 (((~iext(uri_owl_hasSelf, BNODE_x!0, literal_typed(dat_str_true, uri_xsd_boolean))) | (~iext(uri_owl_onProperty, BNODE_x!0, uri_rdf_type)) | ![X: $i] : (icext(BNODE_x!0, X) <=> iext(uri_rdf_type, X, X))) <=> (![X: $i] : (icext(BNODE_x!0, X) <=> iext(uri_rdf_type, X, X)) | (~iext(uri_owl_onProperty, BNODE_x!0, uri_rdf_type)) | (~iext(uri_owl_hasSelf, BNODE_x!0, literal_typed(dat_str_true, uri_xsd_boolean))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 (((~![Z: $i, P: $i, V: $i] : ((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))) | ((~iext(uri_owl_hasSelf, BNODE_x!0, literal_typed(dat_str_true, uri_xsd_boolean))) | (~iext(uri_owl_onProperty, BNODE_x!0, uri_rdf_type)) | ![X: $i] : (icext(BNODE_x!0, X) <=> iext(uri_rdf_type, X, X)))) <=> ((~![Z: $i, P: $i, V: $i] : ((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))) | (![X: $i] : (icext(BNODE_x!0, X) <=> iext(uri_rdf_type, X, X)) | (~iext(uri_owl_onProperty, BNODE_x!0, uri_rdf_type)) | (~iext(uri_owl_hasSelf, BNODE_x!0, literal_typed(dat_str_true, uri_xsd_boolean)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 (((~![Z: $i, P: $i, V: $i] : ((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))) | ((~iext(uri_owl_hasSelf, BNODE_x!0, literal_typed(dat_str_true, uri_xsd_boolean))) | (~iext(uri_owl_onProperty, BNODE_x!0, uri_rdf_type)) | ![X: $i] : (icext(BNODE_x!0, X) <=> iext(uri_rdf_type, X, X)))) <=> ((~![Z: $i, P: $i, V: $i] : ((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))) | ![X: $i] : (icext(BNODE_x!0, X) <=> iext(uri_rdf_type, X, X)) | (~iext(uri_owl_onProperty, BNODE_x!0, uri_rdf_type)) | (~iext(uri_owl_hasSelf, BNODE_x!0, literal_typed(dat_str_true, uri_xsd_boolean))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[44, 42])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 ((~![Z: $i, P: $i, V: $i] : ((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))) | ((~iext(uri_owl_hasSelf, BNODE_x!0, literal_typed(dat_str_true, uri_xsd_boolean))) | (~iext(uri_owl_onProperty, BNODE_x!0, uri_rdf_type)) | ![X: $i] : (icext(BNODE_x!0, X) <=> iext(uri_rdf_type, X, X)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 ((~![Z: $i, P: $i, V: $i] : ((~iext(uri_owl_hasSelf, Z, V)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (icext(Z, X) <=> iext(P, X, X)))) | ![X: $i] : (icext(BNODE_x!0, X) <=> iext(uri_rdf_type, X, X)) | (~iext(uri_owl_onProperty, BNODE_x!0, uri_rdf_type)) | (~iext(uri_owl_hasSelf, BNODE_x!0, literal_typed(dat_str_true, uri_xsd_boolean)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (![X: $i] : (icext(BNODE_x!0, X) <=> iext(uri_rdf_type, X, X))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[47, 41, 22, 21])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 ((~![X: $i] : (icext(BNODE_x!0, X) <=> iext(uri_rdf_type, X, X))) | (icext(BNODE_x!0, uri_ex_c) <=> iext(uri_rdf_type, uri_ex_c, uri_ex_c))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 (icext(BNODE_x!0, uri_ex_c) <=> iext(uri_rdf_type, uri_ex_c, uri_ex_c)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 ((~(icext(BNODE_x!0, uri_ex_c) <=> iext(uri_rdf_type, uri_ex_c, uri_ex_c))) | (~icext(BNODE_x!0, uri_ex_c)) | iext(uri_rdf_type, uri_ex_c, uri_ex_c)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 ((~icext(BNODE_x!0, uri_ex_c)) | iext(uri_rdf_type, uri_ex_c, uri_ex_c)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (~icext(BNODE_x!0, uri_ex_c)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[52, 1])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 (iext(uri_owl_complementOf, uri_ex_c, BNODE_x!0)),
% 0.21/0.40 inference(and_elim,[status(thm)],[20])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 (^[Z: $i, C: $i] : refl(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[58, 56])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (^[Z: $i, C: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(rewrite((icext(Z, X) <=> (~icext(C, X))) <=> (~(icext(C, X) <=> icext(Z, X)))), rewrite((~(icext(C, X) <=> icext(Z, X))) <=> (~(icext(C, X) <=> icext(Z, X)))), ((icext(Z, X) <=> (~icext(C, X))) <=> (~(icext(C, X) <=> icext(Z, X)))))), (![X: $i] : (icext(Z, X) <=> (~icext(C, X))) <=> ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))), (((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))) <=> ((ic(Z) & ic(C)) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))), rewrite(((ic(Z) & ic(C)) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) <=> (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))), (((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))) <=> (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))), ((iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> (iext(uri_owl_complementOf, Z, C) => (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))), rewrite((iext(uri_owl_complementOf, Z, C) => (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))), ((iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 (![Z: $i, C: $i] : (iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.41 tff(65,axiom,(![Z: $i, C: $i] : (iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_bool_complementof_class')).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.41 tff(68,plain,(
% 0.21/0.41 ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[67])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, uri_ex_c, BNODE_x!0)) | (~((~![X: $i] : (~(icext(BNODE_x!0, X) <=> icext(uri_ex_c, X)))) | (~ic(BNODE_x!0)) | (~ic(uri_ex_c)))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | (~iext(uri_owl_complementOf, uri_ex_c, BNODE_x!0)) | (~((~![X: $i] : (~(icext(BNODE_x!0, X) <=> icext(uri_ex_c, X)))) | (~ic(BNODE_x!0)) | (~ic(uri_ex_c)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 (((~iext(uri_owl_complementOf, uri_ex_c, BNODE_x!0)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_x!0)) | (~![X: $i] : (~(icext(BNODE_x!0, X) <=> icext(uri_ex_c, X))))))) <=> ((~iext(uri_owl_complementOf, uri_ex_c, BNODE_x!0)) | (~((~![X: $i] : (~(icext(BNODE_x!0, X) <=> icext(uri_ex_c, X)))) | (~ic(BNODE_x!0)) | (~ic(uri_ex_c)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, uri_ex_c, BNODE_x!0)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_x!0)) | (~![X: $i] : (~(icext(BNODE_x!0, X) <=> icext(uri_ex_c, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, uri_ex_c, BNODE_x!0)) | (~((~![X: $i] : (~(icext(BNODE_x!0, X) <=> icext(uri_ex_c, X)))) | (~ic(BNODE_x!0)) | (~ic(uri_ex_c))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[72])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, uri_ex_c, BNODE_x!0)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_x!0)) | (~![X: $i] : (~(icext(BNODE_x!0, X) <=> icext(uri_ex_c, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | (~iext(uri_owl_complementOf, uri_ex_c, BNODE_x!0)) | (~((~![X: $i] : (~(icext(BNODE_x!0, X) <=> icext(uri_ex_c, X)))) | (~ic(BNODE_x!0)) | (~ic(uri_ex_c)))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[73, 71])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, uri_ex_c, BNODE_x!0)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_x!0)) | (~![X: $i] : (~(icext(BNODE_x!0, X) <=> icext(uri_ex_c, X)))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | (~iext(uri_owl_complementOf, uri_ex_c, BNODE_x!0)) | (~((~![X: $i] : (~(icext(BNODE_x!0, X) <=> icext(uri_ex_c, X)))) | (~ic(BNODE_x!0)) | (~ic(uri_ex_c))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 (~((~![X: $i] : (~(icext(BNODE_x!0, X) <=> icext(uri_ex_c, X)))) | (~ic(BNODE_x!0)) | (~ic(uri_ex_c)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[76, 70, 54])).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 (((~![X: $i] : (~(icext(BNODE_x!0, X) <=> icext(uri_ex_c, X)))) | (~ic(BNODE_x!0)) | (~ic(uri_ex_c))) | ![X: $i] : (~(icext(BNODE_x!0, X) <=> icext(uri_ex_c, X)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 (![X: $i] : (~(icext(BNODE_x!0, X) <=> icext(uri_ex_c, X)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 ((~![X: $i] : (~(icext(BNODE_x!0, X) <=> icext(uri_ex_c, X)))) | (~(icext(BNODE_x!0, uri_ex_c) <=> icext(uri_ex_c, uri_ex_c)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 (~(icext(BNODE_x!0, uri_ex_c) <=> icext(uri_ex_c, uri_ex_c))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 ((icext(BNODE_x!0, uri_ex_c) <=> icext(uri_ex_c, uri_ex_c)) | icext(BNODE_x!0, uri_ex_c) | icext(uri_ex_c, uri_ex_c)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 (icext(BNODE_x!0, uri_ex_c) | icext(uri_ex_c, uri_ex_c)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[83, 53, 13])).
% 0.21/0.41 tff(85,plain,(iext(uri_rdf_type, uri_ex_c, uri_ex_c)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 ((~(iext(uri_rdf_type, uri_ex_c, uri_ex_c) <=> icext(uri_ex_c, uri_ex_c))) | (~iext(uri_rdf_type, uri_ex_c, uri_ex_c)) | icext(uri_ex_c, uri_ex_c)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 ((~iext(uri_rdf_type, uri_ex_c, uri_ex_c)) | icext(uri_ex_c, uri_ex_c)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[86, 10])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 (icext(uri_ex_c, uri_ex_c)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[87, 85])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 ((~(icext(BNODE_x!0, uri_ex_c) <=> iext(uri_rdf_type, uri_ex_c, uri_ex_c))) | icext(BNODE_x!0, uri_ex_c) | (~iext(uri_rdf_type, uri_ex_c, uri_ex_c))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 (icext(BNODE_x!0, uri_ex_c) | (~iext(uri_rdf_type, uri_ex_c, uri_ex_c))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[89, 50])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 (icext(BNODE_x!0, uri_ex_c)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[90, 85])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 ((icext(BNODE_x!0, uri_ex_c) <=> icext(uri_ex_c, uri_ex_c)) | (~icext(BNODE_x!0, uri_ex_c)) | (~icext(uri_ex_c, uri_ex_c))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 ((~icext(BNODE_x!0, uri_ex_c)) | (~icext(uri_ex_c, uri_ex_c))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[92, 81])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[93, 91, 88])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------